Common Core Mathematics 7 (CCM-7) Unit 1 Starting Points
Unit 1: The Number System
Essential Questions:
o Can you reverse the order of rational numbers when performing any operation and still
get the same answer?
o How do operations with integers compare to operations with rational numbers?
o How does the opposite of n differ from the absolute value of n?
o What is the definition of the properties? How are properties applied to solving problems?
o How can the operations with integers be represented conceptually?
o What happens when rational numbers are converted to decimals?
o What are complex fractions?
o How is the order of operations applied to problems dealing with rational numbers?
Curriculum Standards:
Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
7.NS.A.1. Apply and extend previous understandings of addition and subtraction to add and subtract
rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0.
b. Understand p + q as the number located a distance (absolute value of q) from p, in the positive or
negative direction depending on whether q is positive or negative. Show that a number and its
opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing
real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show
that the distance between two rational numbers on the number line is the absolute value of their
difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
7.NS.A.2. Apply and extend previous understandings of multiplication and division and of fractions to
multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that
operations continue to satisfy the properties of operations, particularly the distributive property,
leading to products such as (-1)(-1)=1 and the rules for multiplying signed numbers. Interpret
products of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient
of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (p)/(q) = (p)/(-q). Interpret quotients of rational numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a
rational number terminates in 0s or eventually repeats.
7.NS.A.3. Solve real-world and mathematical problems involving the four operations with rational
numbers.
7.EE.A.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
Approximate Unit Length: 45 days
Standard(s)
7.NS.A.1.a
7.NS.A.1.b
Days
2-3
Notes
Big Ideas:
Describe situations in which opposite quantities combine to
make zero.
Zero Pairs
Additive Inverse
Determine the absolute value for a given number.
Resources:
 Task: And the Winner Is…
Assessment Items:
 Illustrative Mathematics: Comparing Freezing Points
 Illustrative Mathematics: Distances on a Number
Line 2
 Illustrative Mathematics: Operations on a Number
Line

7.NS.A.1.b
7.NS.A.1.c
7.NS.A.2.d
13-17
Big Ideas:
Add and subtract integers.
Add and subtract integers in the context of a real-world
problem.
Resources:
 NCTM Illuminations: Volt Meter
 NCTM Illuminations: Zip, Zilch, Zero
 Lesson: Time Zone Challenge
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed
on PARCC and is also a fluency standard. Adding,
subtracting, multiplying, and dividing rational numbers is the
culmination of numerical work with the four basic
operations. Because there are no specific standards for
rational number arithmetic in later grades and because so
much other work in Grade 7 depends on rational number
arithmetic, fluency with rational number arithmetic should be
the goal in Grade 7.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
Assessment Items:
 Illustrative Mathematics: Distances Between Houses
 Illustrative Mathematics: Equivalent Fractions
Approach to Non-Repeating Decimals
 Illustrative Mathematics: Repeating Decimal as
Approximation
7.NS.A.2.a
7.NS.A.2.b
2-3
Big Ideas:
Multiply and divide integers.
Multiply and divide integers in the context of a real-world
problem.
Resources:
 Lesson: Dividing Integers
7.NS.A.3
7.EE.A.1
3-4
Big Ideas:
Simplify expressions with 4 integer operations.
Estimate solutions given a real-world context.
Simplify an expression given a real-world context using 4
integer operations.
Simplify an expression using the order of operations.
Assessment Items:
 Illustrative Mathematics: Sharing Prize Money
7.NS.A.1.b
7.NS.A.1.c
5-8
Big Ideas:
Convert a rational number to a decimal using long division.
Add and subtract rational numbers.
Add and subtract rational numbers in the context of a realworld problem.
Resources:
 Lesson: Introduction to adding and subtracting
rational numbers
 Lesson: Adding and Subtracting rational numbers
 Weidemann, W., Mikovich, A.K., & Braddockhunt,
J. (December 2001). "Using a Lifeline to give
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
Rational Numbers a Personal Touch." Mathematics
Teaching in the Middle School. Vol. 7. No. 4. p. 210215.
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed
on PARCC and is also a fluency standard. Adding,
subtracting, multiplying, and dividing rational numbers is the
culmination of numerical work with the four basic
operations. In Grade 7, students will add, subtract, multiply,
and divide within the system of rational numbers. Because
there are no specific standards for rational number arithmetic
in later grades and because so much other work in Grade 7
depends on rational number arithmetic, fluency with rational
number arithmetic should be the goal in Grade 7.
7.NS.A.2.a
7.NS.A.2.b
2-3
Big Ideas:
Multiply and divide rational numbers.
Multiply and divide rational numbers in the context of a realworld problem.
Resources:
 Lesson: The meaning of multiplying fractions with
visuals
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed
on PARCC and is also a fluency standard. Adding,
subtracting, multiplying, and dividing rational numbers is the
culmination of numerical work with the four basic
operations. In Grade 7, students will add, subtract, multiply,
and divide within the system of rational numbers. Because
there are no specific standards for rational number arithmetic
in later grades and because so much other work in Grade 7
depends on rational number arithmetic, fluency with rational
number arithmetic should be the goal in Grade 7.
7.NS.A.3
7.EE.A.1
6-7
Big Ideas:
Simplify expressions with 4 integer operations.
Estimate solutions given a real-world context.
Simplify an expression given a real-world context using 4
integer operations.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
Simplify an expression using the order of operations.
Focus on order of operations involving rational numbers.
Resources:
 Task: Triple Triumph
 Lesson: Iced Tea Stand
 NCTM Illuminations: Mango Problem
Assessment Limit/Clarification:
This standard is part of the major content cluster assessed
on PARCC. When students work toward meeting this
standard (which is closely connected to 7.NS.A.1 and
7.NS.A.2), they consolidate their skill and understanding of
addition, subtraction, multiplication, and division of rational
numbers.
Assessment Items:
 PARCC Prototype Items: Anne’s Family Trip
 PARCC Prototype Items: School Supplies
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.